光滑流形的一个调节器和一个指标定理
A regulator for smooth manifolds and an index theorem
摘要：
对于维数<d的光滑流形X，我们构造了一个从X上光滑函数代数的d次代数K理论群到X上系数为C/Z的d-1次拓扑K理论的同态.这个映射推广了Suslin用来计算C的代数K理论的挠子群的映射（X=* 的情况）。本文提出并部分证明了一个猜想，该猜想一方面将上述映射的合成与X上Dirac算子的K-同调类的求值进行了比较，另一方面将其与d-可和Fredholm模的Connes-Karoubi乘法特征进行了比较.
英文摘要：
For a smooth manifold X of dimension <d we construct a homomorphism from the algebraic K-theory group in degree d of the algebra of smooth functions on X to the degree -d-1 topological K-theory of X with coefficients in C/Z. This map generalizes the map used by Suslin in order to calculate the torsion subgroup of algebraic K-theory of C (the case X=*). We state and partially prove a conjecture which compares the composition of the map above with the evaluation against the K-homology class of a Dirac operator on X on the one hand, and the Connes-Karoubi multiplicative character of the associated d-summable Fredholm module on the other.
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